PHYSICS: C. BARUS 
667 
right corresponds to the reflected ray m'Pi on the left both terminating 
in the common wave front Piqs before entering the telescope. 
Let n'P2 
= c' 
= & sin / cos a sin ( 
a) 
= c 
= b sin ^ / cos a sin ( 
^ + 
a) 
P4 
= z' 
= b sin a sin j8 / sin ( 
^ - 
cd 
tq 
= z 
= & sin a sin jS / sin ( 
a) 
and nn' 
= X 
= b sin a / sin {(3 — 
a) 
mm' 
= y 
= b sin a / sin (jS + 
a) 
since the orginal angles at the ends of the base are j8 and the rotation 
a. The angles between incident and reflected rays are respectively 
i8 - 2 a at /3 + 2 « at w', 90° - 2 a at P2 and 90° + 2 a at Pi. 
Finally b has changed to b' on the left and b" on the right. 
The rays however do not reach the plane of symmetry but are re- 
flected by the faces of the right angled prism and this may be sketched 
in apart from size, in the rotated position (angle a) at Pipp' . The 
path of the reflected rays from n' is now n'rs and from m\ m'Pi, before 
they meet in the common wave front Piqs. Hence the intercepts 
rP^ = w = {z -\- z') / cos a (sin a + cos a) 
rs = V = {z -\- z') (cos a — sin a) / (sin a + cos a) 
will enter in treating the path differences. On the left the rays have 
not been disturbed. 
If we take the direct case first the orignal path difference SnP and 
SmP may be regarded zero or n and m in the same phase. On rotation 
therefore (angle a) the path difference is equivalent to the equation 
n \ = c' — c — {w — v) -\- X y 
If the above equivalents are inserted, this equation though very com- 
plicated, may to the second order of small quantities, be reduced to a 
form which, since a and 90° — ^ are small angles for practical purposes 
may be abbreviated to {n, order of interference). 
7l\ = 2ba-2ba^^2b^a/d 
The three terms correspond to the xy, wv and cc' effect. 
In the case of reversed ray (fig. 2) we may consider the points m' 
and n' in the same phase. Hence the original path difference (a = 0) 
is X — y. The path difference after rotation c' — w -\- v — c. The 
total change of path difference due to rotation is thus given by 
n\ = c' — c — {w — v)— x + y 
